Rx Array Research Articles

RF coil design strategies for improving SNR at the ultrahigh magnetic field of 10.5T.

Toward pushing the boundaries of ultrahigh fields for human brain imaging, we wish to evaluate experimentally achievable SNR relative to ultimate intrinsic SNR (uiSNR) at 10.5T, develop design strategies toward approaching the latter, quantify magnetic field-dependent SNR gains, and demonstrate the feasibility of whole-brain, high-resolution human brain imaging at this uniquely high field strength. A dual row 16-channel self-decoupled transmit (Tx) and receive (Rx) array was developed for 10.5T using custom Tx/Rx switches. A 64-channel receive-only array was built to fit into the 16-channel Tx/Rx array. Electromagnetic modeling and experiments were used to define safe operational power limits. Experimental SNR was evaluated relative to uiSNR at 10.5T and 7T. The 64-channel Rx array alone captured approximately 50% of the central uiSNR at 10.5T, while an identical array developed for 7T captured about 76% of uiSNR at 7T. The 16-channel Tx/80-channel Rx configuration brought the fraction of uiSNR captured at 10.5T to levels comparable to the 64-channel Rx array at 7T. SNR data displayed an approximate dependence over a large central region when evaluated in the context of uiSNR. Whole-brain, high-resolution -weighted and T1-weighted anatomical and gradient-recalled-echo BOLD-EPI functional MRI images were obtained at 10.5T for the first time with such an advanced array. We demonstrated the ability to approach the uiSNR at 10.5T over the human brain, achieving large SNR gains over 7T, currently the most commonly used ultrahigh-field platform. Whole-brain, high-resolution anatomical and EPI-based functional MRI data were obtained at 10.5T, illustrating the promise of greater than 10T fields in studying the human brain.

A birdcage transmit, 24-channel conformal receive array coil for sensitive 31P magnetic resonance spectroscopic imaging of the human brain at 7 T.

Phosphorus (31P) magnetic resonance spectroscopic imaging (MRSI) can serve as a critical tool for more direct quantification of brain energy metabolism, tissue pH, and cell membrane turnover. However, the low concentration of 31P metabolites in biological tissue may result in low signal-to-noise ratio (SNR) in 31P MRS images. In this work, we present an innovative design and construction of a 31P radiofrequency coil for whole-brain MRSI at 7 T. Our coil builds on current literature in ultra-high field 31P coil design and offers complete coverage of the brain, including the cerebellum and brainstem. The coil consists of an actively detunable volume transmit (Tx) resonator and a custom 24-channel receive (Rx) array. The volume Tx resonator is a 16-rung high-pass birdcage coil. The Rx coil consists of a 24-element phased array composed of catered loop shapes and sizes built onto a custom, close-fitting, head-shaped housing. The Rx array was designed to provide complete coverage of the head, while minimizing mutual coupling. The Rx configuration had a mean reflection coefficient better than -20 decibels (dB) when the coil was loaded with a human head. The mean mutual coupling ( ) among Rx elements, when loaded with a human head, was -16 dB. In phantom imaging, the phased array produced a central SNR that was 4.4-fold higher than the corresponding central SNR when operating the 31P birdcage as a transceiver. The peripheral SNR was 12-fold higher when applying the optimized phased array. In vivo 3D 31P MRSI experiments produced high-quality spectra in the cerebrum gray and white matter, as well as in the cerebellum. Characteristic phosphorus metabolites related to adenosine triphosphate metabolism and cell membrane turnover were distinguishable across all brain regions. In summary, our results demonstrate the potential of our novel coil for accurate, whole-brain 31P metabolite quantification.

A Single-Board Integrated Millimeter-Wave Asymmetric Full-Digital Beamforming Array for B5G/6G Applications

In this article, a single-board integrated millimeter-wave (mm-Wave) asymmetric full-digital beamforming (AFDBF) array is developed for beyond-fifth-generation (B5G) and sixth-generation (6G) communications. The proposed integrated array effectively addresses the challenge of arranging a large number of ports in a full-digital array by designing vertical connections in a three-dimensional space and successfully integrating full-digital transmitting (Tx) and receiving (Rx) arrays independently in a single board. Unlike the traditional symmetric array, the proposed asymmetric array is composed of an 8 × 8 Tx array arranged in a square shape and an 8 + 8 Rx array arranged in an L shape. The center-to-center distance between two adjacent elements is 0.54λ0 for both the Tx and Rx arrays, where λ0 is the free-space wavelength at 27 GHz. The proposed AFDBF array possesses a more compact structure and lower system hardware cost and power consumption compared with conventional brick-type full-digital arrays. In addition, the energy efficiency of the proposed AFDBF array outperforms that of a hybrid beamforming array. The measurement results indicate that the operating frequency band of the proposed array is 24.25–29.50 GHz. An eight-element linear array within the Tx array can achieve a scanning angle ranging from −47° to +47° in both the azimuth and the elevation planes, and the measured scanning range of each eight-element Rx array is –45° to +45°. The measured maximum effective isotropic radiated power (EIRP) of the eight-element Tx array is 43.2 dBm at 28.0 GHz (considering the saturation point). Furthermore, the measured error vector magnitude (EVM) is less than 3% when 64-quadrature amplitude modulation (QAM) waveforms are used.

Thinned Randomized 27–29 GHz TX and RX Arrays With Low Sidelobe Levels for Radars and 5G Communications

Thinned Randomized 27–29 GHz TX and RX Arrays With Low Sidelobe Levels for Radars and 5G Communications

Compact and Highly Efficient Short-Range Radar for Advanced Driver Assistant Systems

A compact and highly efficient 24 GHz circularly polarized (CP) short range radar (SRR) module is proposed. The proposed SRR is configured by highly integrated right-hand CP (RHCP) transmit (Tx) and left-hand CP (LHCP) receive (Rx) antenna arrays and a single 4-Tx and 4-Rx CMOS radar IC. The Tx RHCP and Rx LHCP antenna elements are coplanarly and concentrically arranged to form a 2 × 2 configuration for each Tx and Rx. The concentric integration can effectively increase the area efficiency while maintaining a high Tx-to-Rx isolation due to the opposite CP. Further, the radar IC is fabricated with TSMC 65 nm process and directly mounted on the back of the complete module. Each Tx and Rx channels of the IC are connected to each Tx and Rx array elements through multilayered feed network and bonding wires. Then, the SRR is operated as one Tx with 1 × 4 array and four Rx with individual antennas. Lastly, the complete CP SRR module is successfully verified at 24 GHz with a detection range from 1 m to 20 m.

Efficiency Bound Estimation for a Practical Microwave and mmWave Wireless Power Transfer System Design

In this study, we present an efficient method to find the power transfer efficiency (PTE) bound for practical microwave and mmWave wireless power transfer (MPT) systems composed of transmitter (Tx) and receiver (Rx) array antennas. The PTE bound of the MPT system is obtained by formulating it as a convex optimization problem (CVP) that maximizes the power received at the Rx array under the transmit power constraint. The channel state information (CSI) between each element of the Tx and the Rx is the input parameter of the proposed CVP. The CSI is estimated using the Friis transmission equation and the active element pattern of the array antenna because the Tx and the Rx are assumed to be large arrays. For an MPT system designed at 10 GHz and 24 GHz, the estimated PTE bound is compared to those in previous studies while varying the distance and tilted angle between the Tx and the Rx. The computation times required for the methods are compared. The numerical results show that the proposed method provides a faster and more accurate PTE bound without full electromagnetic simulation of the MPT system consisting of Tx and Rx array antennas. This study's results will serve as guidelines for practical MPT system design in the future.

60 GHz RF module with beam-steering optimization algorithm for high data rate access and backhaul communications

This paper presents an 802.11ad-based radio frequency module for high data rate fixed wireless access and backhaul communications. The transceiver chip is manufactured in SiGe BiCMOS technology covering 57–71 GHz, providing 16 RX and 16 TX paths with combined output power of more than 20 dBm. The chip is packaged using embedded wafer-level BGA technology of the size 12.6times 12.6times 0.8~{text{ mm }}^3 and employs advanced dielectric materials with 2 metallic redistribution layers. The package integrates the transceiver chip with RX and TX high gain PCB antenna arrays, allowing effective isotropic radiated power (EIRP) of more than 40 dBm. Beam steering is achieved in ± 50^{circ } by the transceiver through providing appropriate weights to the antenna arrays. The paper presents generation of beamforming lookup table along with optimization of the power distribution to the array. This optimization results in flattening of the EIRP over the whole beam-steering range and frequency bandwidth. The module allows for data rates up to 10 Gbps by employing full-channel 128 QAM and half-channel 256 QAM single-carrier modulation.

Sparse Automotive MIMO Radar for Super-Resolution Single Snapshot DOA Estimation With Mutual Coupling

A novel sparse automotive multiple-input multiple-output (MIMO) radar configuration is proposed for low-complexity super-resolution single snapshot direction-of-arrival (DOA) estimation. The physical antenna effects are incorporated in the signal model via open-circuited embedded-element patterns (EEPs) and coupling matrices. The transmit (TX) and receive (RX) array are each divided into two uniform sparse sub-arrays with different inter-element spacings to generate two MIMO sets. Since the corresponding virtual arrays (VAs) of both MIMO sets are uniform, the well-known spatial smoothing (SS) algorithm is applied to suppress the temporal correlation among sources. Afterwards, the co-prime array principle between two spatially smoothed VAs is deployed to avoid DOA ambiguities. A performance comparison between the sparse and conventional MIMO radars with the same number of TX and RX channels confirms a spatial resolution enhancement. Meanwhile, the DOA estimation error due to the mutual coupling (MC) is less pronounced in the proposed sparse architecture since antennas in both TX and RX arrays are spaced larger than half wavelength apart.

MIMO Radar Array Antenna with Transmit-Receive Subarrays

Unlike the PMIMO radar, the transmit-receive (Tx-Rx) subarrays MIMO (TRSM) radar uses overlaping subarrays in Tx and Rx array so that it simultaneously combines the main advantage of the phased array radar (PA) i.e., high directional coherent gain, and the main advantage of the MIMO radar i.e., high waveform diversity gain. This paper has derived the radar performance formula such that Tx-Rx gain and SINR. The approach aims to overcome the beam shape loss, increase the transmit-receive gain, minimize the maximum peak sidelobe levels, narrow the half power beamwidth, increase directivity, and increase signal-to-noise-plus-interference ratio (SINR). This radar's performance is compared to the PMIMO radar in various methods such as equal subarrays, unequal subarrays, and optimum partitioning, the PA radar, and the MIMO radar. The numerical simulation and evaluation results show that the proposed radar has several advantages such as lowest the peak sidelobe level, narrow the half power beamwidth, and high directivity, so it is very robust against interference effects. When compared to the OPPM radar, as representative of the best-performing radars, this radar has an average performance improvement of MPSLL, directivity, and HPBW which are 21.5 dB, 2 dB, and 0.45 deg, respectively.

A 28-GHz Beam-Space MIMO RX With Spatial Filtering and Frequency-Division Multiplexing-Based Single-Wire IF Interface

The evolution of mm-wave phased array receivers (RX) to MIMO RX promises multi-beamforming and improved capacity. Although digital beamforming (DBF) provides the highest flexibility, digitization in the beam space as opposed to element space enables ADC digitization scalability with number of beams ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\le $ </tex-math></inline-formula> 4) and spatial filtering prior to the ADC. mm-Wave MIMO arrays must also address the challenge of increased IO routing while supporting dense fill-factors with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda /2$ </tex-math></inline-formula> antenna spacing. In this work, an MIMO beam-space RX array architecture with simultaneous spatial filtering and single wire frequency-domain multiplexing (FDM) is presented. The reconfigurable weighted multi-phase mixing based beam-space RX scheme achieves both: 1) multi-beam formation/spatial filtering and 2) FDM of multiple beam-space outputs, preserving full MIMO field-of-view while ensuring a single IF interface. A 28-GHz four-element RX prototype demonstrates the proposed architecture in 65-nm CMOS. The IC occupies only 3.4 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 3.1 mm for a four-element MIMO 28-GHz array and can form four independent beams with >400-MHz 3-dB BW and FDM on to a single IF interface. The array consumes 450 mW and achieves >27-dB beam-to-beam isolation over 150-MHz BW, while consuming 28.1 mW/stream/beam for 28 GHz. Concurrent MIMO measurements with two wireless 28-GHz beams are shown at 400 Mb/s (100 Msps, 16QAM) data rate demonstrating mm-wave MIMO operation.

A 28-GHz Full-Duplex Phased Array Front-End Using Two Cross-Polarized Arrays and a Canceller

This article proposes a 28-GHz full-duplex (FD) phased arrays, which consists of 64-element transmitting and receiving arrays, and a 28-GHz radio frequency (RF) canceller. The phased arrays are designed with $2\times 2$ beamformer chips, and the transmitter (TX) and receiver (RX) arrays are oriented to have cross polarized configurations for high isolation. The 28-GHz RF canceller is based on an identical $2\times 2$ beamformer chip with two external different delay taps. Since the canceller is located at the input and output ports of arrays instead of antennas, it cannot eliminate the nonlinearities and noises in the phased arrays. Therefore, these nonlinearities and noise in the TX and RX arrays are experimentally analyzed to demonstrate that the proposed cross-polarized arrays have enough isolation to achieve suppression to the level of the RX noise floor. The FD phased-array system at 28.5–29.5 GHz has 57-dB isolation between the TX input and RX output ports, where the cross-polarization improves 10-dB isolation comparing to co-polarization and the RF canceller provide additional 10-dB self-interference (SI) suppression. Also, the nonlinearities and noise components of the received SI signals are lower than the noise floor at the output of the RX array. The system requires only 15.5-dB of additional digital cancellation to reduce the SI to the RX noise floor of 1-GHz bandwidth while maintaining the transmitting EIRP at 41 dBm.

Antenna isolation method using sub-array structure with soft-surface for Tx/Rx separated FDD hybrid beamforming system

The FDD method is normally used for the stability of the Tx and the Rx links in a fast-varying channel. It is required to physically separate the Tx and Rx arrays for independent Tx and Rx beam control. In this system, it is important to reduce the Tx self-interference (SI) that causes the problem of active element saturation and ADC dynamic range in the Rx beamformer. To suppress Tx SI, we proposed two simple techniques. The first is the general soft-surface which attenuates the surface current flow from the Tx tile array to the Rx array. The second is the sub-array structure of the Rx hybrid beamforming system. Based on the Cauchy–Schwartz inequality, the electrical sum by the sub-array acts as a destructive interference of the complex SI signals, and it can be shown as an additional isolation effect. The proposed idea was validated through measurement.

LUT-Based Focal Beamforming System Using 2-D Adaptive Sequential Searching Algorithm for Microwave Power Transfer

This paper presents a look-up table (LUT)-based focal beamforming system that can effectively transmit RF power up to mid-range distances (≤ 3 m) including when the Rx is in the near-field zones. The Tx elements control and radiate signals for the Rx even at the near-field zone ensuring the received signals are in-phase. Since the proposed system uses a LUT for storing the phase sets of the signals for the Tx elements, it requires only very simple hardware and a very simple adaptive control algorithm compared to conventional retroreflective method. In order to track the moving Rx, a 2-D adaptive sequential searching algorithm is proposed. The system can find the optimum phase set by sequentially searching the phase sets for a pre-determined 2-D area. The LUT of the phase sets are generated using geometric analysis over the entire 2-D area where the Rx could be located. To verify the proposed method, a 5.2 GHz mid-range (≤ 3 m) MPT system composed of a 4 × 8 Tx array and a 2 × 3 Rx array was designed and implemented. Using the proposed 2-D adaptive sequential searching algorithm, the optimum phase set for focal beamforming can be quickly found for a given position of the Rx. In our experiments, the results showed an RF power level of 177.8 mW was received at the Rx with a distance of 1 m with a total radiated RF power of 16W. Since the measured received power levels for various Rx positions agree well with the simulation results, the proposed system was proved to be an excellent candidate for the practical application.

A Mm-Wave Wideband MIMO RX With Instinctual Array-Based Blocker/Signal Management for Ultralow-Latency Communication

This article demonstrates a wideband mm-Wave multiple-input–multiple-output (MIMO) receiver (RX) system with cascadable array-based high-order autonomous spatial filters (ASFs) for closed-loop frontend beamforming, achieving “instinctual” (“Instinctual” is defined as an autonomous operation for sensing, controlling, processing signals with ultralow-latency and no backend digital signal processing assist.) management of multiblockers/signals with ultrafast response time. Over a full field-of-view (FoV), the ASFs achieve automatic blocker suppression and desired signal beamforming without prior knowledge on the angle-of-arrival/frequency/modulation and without beam-searching using backend computations. In particular, the ASFs realize frontend blocker suppression and substantially relax the dynamic range requirement of down-stream analog-to-digital converters (ADCs) in digital arrays. Moreover, cascading multiple ASFs can sequentially suppress multiple blockers, essentially achieving the “iterative source localization” DSP algorithm by the frontend hardware. A proof-of-concept 27–41-GHz four-element MIMO RX array is implemented in a 45-nm CMOS silicon-on-insulator (SOI) process to support multistandard 5G links in the future congested/contested electromagnetic (EM) environments. With autonomous cancellation of multiple co-channel wideband blockers, a wideband desired signal can be received with high signal-to-interference-plus-noise ratio (SINR), achieving −28.64-dB error vector magnitude (EVM) for 3-Gb/s 64QAM and −32.73-dB EVM for 0.8-Gb/s 256QAM. The measured MIMO beamforming response time for beam scanning, localization, and computation is $\mu \text{s}$ /stage, enabling 5G and beyond-5G ultralow-latency mm-Wave links.

Air-Coupled Ultrasound Time Reversal (ACU-TR) For Subwavelength Nondestructive Imaging.

Air-coupled ultrasound (ACU) is increasingly used for nondestructive testing (NDT). With ACU, no contact or coupling agent (e.g., water and ultrasound gel) is needed between transducers and test sample, which provides high measurement reproducibility. However, for testing in production, a minimum separation is often necessary between the sample and the transducers to avoid contamination or transducer damage. Due to wave diffraction, the collimation of the ultrasound beam decreases for larger propagation distances, and ACU images become blurred and show lower defect lateral resolution with increasing sample-transducer separation. This is especially critical to thick composites, where large-size planar sources are used to bridge the large ACU transmission loss with good collimation. In this work, ACU reradiation in unbounded media is extended to NDT of multilayered composites. The extended method is named ACU time reversal (ACU-TR) and significantly improves the defect resolution of ACU imaging. With ACU-TR, the complete pressure distribution radiated by large ACU source is measured with point receivers (RXs) in one plane arbitrarily separated from the sample. By applying acoustic holography physics, it is then possible to quantitatively reconstruct the pressure field directly at arbitrary sample defect planes, which compensates for undesired diffraction phenomena and improves minimum detectable defect size, thereby achieving subwavelength lateral resolution. We tested the method on complex wood-based composite samples based on the ACU far-field measurements at a separation of 160 mm between the sample and the RX transducer. With the proposed method, it is possible to detect surface defects as well as inner defects within composite boards. In the future, by using point RX arrays instead of a scanned microphone, both data acquisition and evaluation can be potentially implemented in real time.

Feasibility study of a double resonant 8-channel 1H/ 8-channel 23Na receive-only head coil at 3 Tesla

Sodium (23Na) magnetic resonance imaging (MRI), especially brain applications are increasingly interesting since sodium MRI can provide additional information about tissue viability and vitality. In order to include sodium MRI in the clinical routine, a single RF setup is preferable which provides high sodium sensitivity and full proton performance in terms of signal-to-noise ratio (SNR) and parallel imaging performance. The aim of this work was to evaluate the feasibility of a double resonant receive (Rx) coil array for proton and sodium head MRI. The coil was designed to provide high sodium SNR and full proton performance comparable to commercial coils which are optimized for sodium MRI or for proton MRI, respectively. A measurement setup was built which comprised an 8-channel Rx degenerate Birdcage for sodium imaging and an 8-channel Rx array for proton imaging. The performance of the coil was evaluated against commercial sodium and proton coils using phantom and in-vivo measurements of two healthy volunteers.

High-Isolation Array Antenna Integration for Single-Chip Millimeter-Wave FMCW Radar

By using the second bandgap in mushroom electromagnetic bandgap (EBG) structures, a high isolation can be achieved between transmitting (TX) and receiving (RX) microstrip array antennas integrated with a millimeter-wave single-chip frequency-modulated continuous-wave (FMCW) radar. These EBG structures are much easier to manufacture at millimeter waves as compared to the first bandgap mushroom EBG structures. In addition to improving isolation, the EBG structures are also used to reduce radiation pattern ripples caused by edge diffractions due to surface waves. Experimental validation is performed on antenna level and on the radar system level. For the system-level validation, the antenna arrays have been integrated with a single-chip mm-wave FMCW radar using the bond-wire interconnect technology. Measurement results in the 57–64 GHz band show the TX–RX isolation of 40 dB, which is 15–20 dB better than the isolation between TX and RX arrays without EBG structures. In addition, the radiation pattern ripple caused by edge diffractions is reduced below 3 dB.

Design and measurement of a 5G mmW mobile backhaul transceiver at 28 GHz

High throughput and ultra low latency are the main requirements for fifth generation (5G) mobile broadband communications. Densely populated urban environments require utilization of previously underutilized millimeter wave frequency spectrum for higher data rates. The Ka-band, previously used in satellite applications, is of particular interest to terrestrial 5G mobile networks. New radio solutions are required for these frequencies, such as multiple wireless base stations organized in small cells and highly directional antennas to compensate for higher path loss. Wireless backhaul is predicted to be the most cost-effective and versatile solution to connect 5G base stations to the core network. Wireless backhaul enables flexible and easy installation of 5G base stations in ad hoc networks, supporting large crowd gatherings such as concerts and sports events. In this article, we present an architecture of a wireless backhaul transceiver, which operates on the 26.5–29.5-GHz band. The architecture described in this paper was implemented, and the performance of the receiver (Rx) array has been measured. We also present over-the-air antenna array measurement results using the Rx. The measurement results show that unequal Rx channel gains and antenna gains do not have a significant effect on the shape of the main lobe of the radiation pattern. We have measured a coherence gain of 2.7 dB from two Rx channels that is close to the theoretical value of 3.0 dB. We have achieved a conducted Rx EVM of better than 2% using a 100-MHz 16-QAM modulated signal at 26.5 GHz.

Evaluating the effects of receive-only arrays in specific absorption rate simulations at 3 and 7 T

Specific absorption rate (SAR) simulations are performed for most clinical and research transmit coil configurations. Such simulations allow the determination of limits in transmit power for patient safety. Different human models and coil configurations have been previously investigated using these simulations. However, only a few works have accounted for the effect of the receive (Rx) arrays in the SAR calculations and they have used very specialized setups or simplified detuning modeling of the Rx elements. In this work, we performed electromagnetic simulations using a clinical alike setup for whole-body scans at 3 T and head scans at 7 T. SAR simulations are performed for both setups with and without Rx arrays. A difference below 10% percent was found for max SAR. The maximum difference for the mean SAR values of the 3 T setups remained within 8% and within 15% of the 7 T setup.

Reducing signal‐to‐noise ratio degradation due to coil coupling in a receiver array for 35Cl MRI at 9.4 T: A comparison of matching and decoupling strategies

AbstractNext to conventional magnetic resonance imaging (MRI), which utilizes hydrogen nuclei, other nuclei, so‐called X‐nuclei, are of increasing interest since they can provide additional diagnostic information. However, X‐nuclei MRI is challenging due to the lower Signal‐to‐Noise Ratio (SNR) compared to 1H (35Cl provides approximately 200 000 times lower SNR than 1H). In order to compete with this challenge, the use of high‐field strengths and optimized hardware is crucial. In this work, a transmit‐only receive‐only (TORO) system for 35Cl MRI at a preclinical 9.4 T scanner is presented, composed of a volumetric birdcage coil and a 3 channel Rx array. SNR degradation despite preamplifier decoupling can no longer be neglected since the resonance frequency of 35Cl is low. This paper will prove the SNR degradation due to the coil coupling of the receiver coils for this setup and evaluate three different approaches to mitigate the SNR degradation. The performance of the different approaches is evaluated via single channel and combined SNR maps using phantom measurements. Finally, the SNR maps acquired with the Rx array are compared to the SNR map acquired using the Birdcage coil as a reference.